humancommunicationsfandomcom-20200215-history
Cooperative diversity
Cooperative diversity is a virtual multiple antenna techniques which exploits user diversity by allowing for the destination node to decode the multiple received signal from the relayed and direct nodes in wireless multihop networks. Conventional single hop wireless systems use direct transmission where a receiver node decodes information only based on the received signal from the source node while regarding the relayed signal as interference, whereas the cooperative diversity considers the other signal as contribution. That is, cooperative diversity allows the destination node to decode the information from the combination of two differently received signals from the source and relay nodes. Hence, it can be seen that cooperative diversity is an virtual antenna diversity that uses distributed antennas belonging to different nodes in a wireless network. Note that user cooperation is an alternative definition of cooperative diversity. In user cooperation, we consider an additional fact that each user relays the other user's signal while cooperative diversity can be also achieved by multi-hop relay networking systems. Relaying Strategies Cooperative diversity can be implemented by a few relaying strategies such as the amplify-and-forward, decode-and-forward, and compress-and-forward relaying strategies. Amplify-and-forward The amplify-and-forward strategy allows the relay station amplifies the received signal from the source node and forwards to the destination station Decode-and-forward The decode-and-forward strategy allows the relay station decodes the received signal from the source node, re-encodes and forwards to the destination station Compress-and-forward The compress-and-forward strategy allows the relay station compress the received signal from the source node and forwards to the destination without decoding the signal where Wyner-Ziv coding can be used for optimal compression. System model We consider a wireless relay system that consists of source, relay and destination nodes. It is assumed that the channel is in a half-duplex, orthogonal and amplify-and-forward relaying mode. Differently to the conventional direct transmission system, we exploit a time division relaying function where this system can deliver information with two temporal phases. On the first phase, the source node broadcasts information x_{s} toward both the destination and the relay nodes. The received signal at the destination and the relay nodes are respectively written as: : r_{d,s} = h_{d,s} x_{s} + n_{d,s} \quad : r_{r,s} = h_{r,s} x_{s} + n_{r,s} \quad where h_{d,s} is the channel from the source to the destination nodes, h_{r,s} is the channel from the source to the relay node, n_{r,s} is the noise signal added to h_{r,s} and n_{d,s} is the noise signal added to h_{d,s} . On the second phase, the relay can transmit its received signal to the destination node except the direct transmission mode. Signal Decoding We introduce four schemes to decode the signal at the destination node which are the direct scheme, the non-cooperative scheme, the cooperative scheme and the adaptive scheme. Except the direct scheme, the destination node uses the relayed signal. Direct Scheme In the direct scheme, the destination decodes the data using the signal received from the source node on the first phase where the second phase transmission is omitted so that the relay node is not involved in transmission. The decoding signal received from the source node is written as: : r_{d,s} = h_{d,s} x_{s} + n_{d,s} \quad While the advantage of the direct scheme is its simplicity in terms of the decoding processing, the received signal power can be severely low if the distance between the source node and the destination node is large. Thus, in the following we consider non-cooperative scheme which exploits signal relaying to improve the signal quality. Non-cooperative Scheme In the non-cooperative scheme, the destination decodes the data using the signal received from the relay on the second phase, which results in the signal power boosting gain. The signal received from the relay node which retransmits the signal received from the source node is written as: : r_{d,r} = h_{d,r} r_{r,s} + n_{d,r} = h_{d,r} h_{r,s} x_{s} + h_{d,r} n_{r,s} + n_{d,r} \quad where h_{d,r} is the channel from the relay to the destination nodes and n_{r,s} is the noise signal added to h_{d,r} . The reliability of the decoding can be low since the number of degree of freedom is not increased by signal relaying. the first order since this scheme exploit only the relayed signal. Thus, in the following we consider the cooperative scheme which decodes the combined signal of both the direct and relayed signals. Cooperative Scheme For cooperative decoding, the destination node combines two signals received from the source and the relay nodes which results in the diversity advantage. The whole received signal vector at the destination node can be modeled as: : \mathbf{r} = \quad r_{d,r}^T = \quad h_{d,r} h_{r,s}^T x_{s} + \left\quad \sqrt{|h_{d,r}|^2+1} \right^T n_{d} = \mathbf{h} x_{s} + \mathbf{q} n_{d} where r_{d,s} and r_{d,r} are the signals received at the destination node from the source and relay nodes, respectively. As a linear decoding technique, the destination combines elements of the received signal vector as follows: : y = \mathbf{w}^H \mathbf{r} where \mathbf{w} is the linear combining weight which can be obtained to maximize signal-to-noise ratio (SNR) of the combined signals subject to given the complexity level of the weight calculation. Adaptive Scheme Adaptive scheme selects one of the three modes described above which are the direct, the non-cooperative, and the cooperative schemes relying on the network channel state information and other network parameters. Trade-off It is noteworthy that cooperative diversity can increase the diversity gain at the cost of lossing the wireless resource such as frequency, time and power resources for the relaying phase. Wireless resources are wasted since the relay node uses wireless resources to relay the signal from the source to the destination node. Hence, it is important to remark that there is trade-off between the diversity gain and the waste of the spectrum resource in cooperative diversity. Channel Capacity of Cooperative Diversity In June 2005, A. Høst-Madsen published a paper in-depth analyzing the channel capacity of the cooperative relay network . We assume that the channel from the source node to the relay node, from the source node to the destination node, and from the relay node to the destination node are c_{21} e^{j\varphi_{21}},c_{31} e^{j\varphi_{31}},c_{32} e^{j\varphi_{32}} where the source node, the relay node, and the destination node are denoted node 1, node 2, and node 3, subsequently. The capacity of cooperative relay channels Using the max-flow min-cut theorem yields the upper bound of full duplex relaying : C^+ = \max_{f(X_1,X_2)} \min \{ I(X_1;Y_2,Y_3|X_2), I(X_1,X_2;Y_3)\} where X_1 and X_2 are transmit information at the source node and the relay node respectively and Y_2 and Y_3 are received information at the relay node and the destination node respectively. Note that the max-flow min-cut theorem states that the maximum amount of flow is equal to the capacity of a minimum cut, i.e., dictated by its bottleneck. The capacity of the broadcast channel from X_1 to Y_2 and Y_3 with given X_2 is : \max_{f(X_1,X_2)} I(X_1;Y_2,Y_3|X_2) = \frac{1}{2} \log(1 + (1 - \beta) (c^2_{21} + c^2_{31})P_1 ) while the capacity of the multiple access channel from X_1 and X_2 to Y_3 is : \max_{f(X_1,X_2)} I(X_2,X_2;Y_3) = \frac{1}{2} \log(1 + c^2_{31} P_1 + c^2_{32} P_2 + 2 \sqrt{ \beta c^2_{31} c^2_{32} P_1 P_2}) where \beta is the amount of correlation between X_1 and X_2 . Note that X_2 copies some part of X_1 for cooperative relaying capability. Using cooperative relaying capability at the relay node improves the performance of reception at the destination node. Thus, the upper bound is rewritten as : C^+ = \max_{0 \leq \beta \leq 1} \min \left\{ \frac{1}{2} \log(1 + (1 - \beta) (c^2_{21} + c^2_{31}) P_1), \frac{1}{2} \log(1 + c^2_{31} P_1 + c^2_{32} P_2 + 2 \sqrt{ \beta c^2_{31} c^2_{32} P_1 P_2}) \right\} Achievable rate of a decode-and-forward relay Using a relay which decodes and forwards its captured signal yields the achievable rate as follows: : R_1 = \max_{f(X_1,X_2)} \min \{ I(X_1;Y_2|X_2), I(X_1,X_2;Y_3)\} where the broadcast channel is reduced to the point-to-point channel because of decoding at the relay node, i.e., I(X_1;Y_2,Y_3|X_2) is reduced to I(X_1;Y_2|X_2) . The capacity of the reduced broadcast channel is : \max_{f(X_1,X_2)} I(X_1;Y_2|X_2) = \frac{1}{2} \log(1 + (1 - \beta) c^2_{21} P_1 ). Thus, the achievable rate is rewritten as : R_1 = \max_{0 \leq \beta \leq 1} \min \left\{ \frac{1}{2} \log(1 + (1 - \beta) c^2_{21} P_1), \frac{1}{2} \log(1 + c^2_{31} P_1 + c^2_{32} P_2 + 2 \sqrt{ \beta c^2_{31} c^2_{32} P_1 P_2}) \right\} Time-Division Relaying The capacity of the TD relay channel is upper-bounded by : C^+ = \max_{0 \leq \beta \leq 1} \min \{ C_1^+(\beta), C_2^+(\beta) \} with : C_1^+(\beta) = \frac{\alpha}{2} \log \left( 1 + (c_{31}^2 + c_{21}^2) P_1^{(1)} \right) + \frac{1-\alpha}{2} \log \left( 1 + (1-\beta) c_{31}^2 P_1^{(2)} \right) : C_2^+(\beta) = \frac{\alpha}{2} \log \left( 1 + c_{31}^2 P_1^{(1)} \right) + \frac{1-\alpha}{2} \log \left( 1 + c_{31}^2 P_1^{(2)} + c_{32}^2 P_2 + 2 \sqrt{ \beta C_{31}^2 P_1^{(2)} C_{32}^2 P_2} \right) References See also Systems * Cooperative wireless communications ** Cooperative MIMO ** Wireless ad-hoc network ** Mobile ad-hoc network ** Wireless mesh network *** Mesh network * Wireless community network Technologies * Diversity schemes * Dynamic Single Frequency Networks (DSFN) * Soft handover * Space–time code * Multiple-input multiple-output communications (MIMO) * Multiuser MIMO * Diversity combining * Transmit diversity * Diversity gain External references * A. Sendonaris, E. Erkip, and B. Aazhang, “User Cooperation Diversity Part I and Part II,” IEEE Trans. Commun., vol. 51, no. 11, Nov. 2003, pp. 1927–48. * J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior,” IEEE Trans. Inform. Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004. * S. Valentin, et al., Cooperative wireless networking beyond store-and-forward: Perspectives for PHY and MAC design * Sébastien Simoens, Josep Vidal, Olga Muñoz, COMPRESS-AND-FORWARD COOPERATIVE RELAYING IN MIMO-OFDM SYSTEMS Category:Radio resource management